Chapter 3, Problem 16STP

(a)

To determine

A table that shows the height of the hot air balloon after climbing 1,2,3 and 4 minutes

Answer to Problem 16STP

Thus, the height is 75,90,105,120.

Explanation of Solution

Given:

A hot air balloon was at a height of 60 feet above the ground when it began to ascend and balloon climed at a rate of 15 feet per minute.

Calculation:

To find the table we use follow formula and simplify further as shown below:

TIME	HEIGHT
1	75
2	90
3	105
4	120

  $\begin{array}{c}h=60+15t\\ t=1\\ h=60+15\cdot 1\\ =75\\ t=2\\ h=60+15t\\ =60+15\cdot 2\\ =60+30\\ =90\\ t=3\\ h=60+15t\\ =60+15\cdot 3\\ =60+45\\ =105\\ t=4\\ h=60+15t\\ =60+15\cdot 4\\ =60+60\\ =120\end{array}$

Thus, the height is 75,90,105,120.

(b)

To determine

The algebraic equation.

Answer to Problem 16STP

  $h=60+15t$

Explanation of Solution

Given:

The t represent the time in minutes since the balloon began climbing.

Calculation:

In order to find the algebraic equation for a sequence that can be used to find the height h , of the balloon after t minutes as shown below:

  $h=60+15t$

Thus, the algebraic equation is $h=60+15t$ .

(c)

To determine

The height in feet of the air balloon after climbing for 8 minutes..

Answer to Problem 16STP

  $180\text{feet}$

Explanation of Solution

Given:

  $h=60+15t$

Calculation:

In order to find the height in feet as shown below:

  $\begin{array}{c}h=60+15t\\ h=60+15\cdot 8\\ h=60+120\\ h=180\text{feet}\end{array}$

Thus, the height of the hot balloon after climbing for 8 minutes is $180\text{feet}$ .